Mathematics - Sequence & Series Question with Solution | TestHub

If $d$ be the common difference, then $$\begin{array}{rl}m& =a_4-a_7+a_{10}=a_4-a_7+a_7+3\mathrm{d}=a_7\\ {\mathrm{S}}_{13}& =\frac{13}{2}\left[a_1+a_{13}\right]=\frac{13}{2}\left[a_1+a_7+6d\right]\\ & =\frac{13}{2}\left[2a_7\right]=13a_7=13\mathrm{m}\end{array}$$